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2 years ago

The product of −2 and a number x is greater than 30. Whats the solution of the inequality.

Mathematics

1 answer:

marta [7]2 years ago

5 0

Answer: x < -15

Step-by-step explanation:

(-2)*(x) > 30

x < -15 The inequality reverses direction when a negative number is used in the manipulation (we divided by -2).

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Solve by simplifying the problem. There are 18 students in Mr. Alvarez’s art class. Throughout the year, every student must pair

Alla [95]

We are given with an 18 student class that is working a project worked by pairs. Each pair works on a project. In this case, there are 9 teams of 2 individuals working on a single project. Hence for a year or school year, there are 9 projects accomplished each time.

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3 years ago

Can someone help please

Naddika [18.5K]

Answer:

I believe the answer is 8 because 8 can go in both 64 and 40.

Step-by-step explanation:

If you divide 64 by 8 then you get 8 and if you divide 40 by 5 you also get 8.

3 0

2 years ago

Read 2 more answers

Find an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = 4x − 4 at (1, 0).

larisa86 [58]

We are given the following:
- parabola passes to both (1,0) and (0,1)
 - slope at x = 1 is 4 from the equation of the tangent line 

First, we figure out the value of c or the y intercept, we use the second point (0, 1) and substitute to the equation of the parabola. When x = 0, y = 1. So, c should be equal to 1. The parabola is y = ax^2 + bx + 1 

Now, we can substitute the point (1,0) into the equation,
0 = a(1)^2 + b(1) + 1
0 = a + b + 1
a + b = -1 

The slope at x = 1 is equal to 4 which is equal to the first derivative of the equation.
We take the derivative of the equation ,
y = ax^2 + bx + 1
y' = 2ax + b

x = 1, y' = 2
4 = 2a(1) + b
4 = 2a + b 

So, we have two equations and two unknowns, 
2a + b = 4 
a + b = -1

Solving simultaneously,
a = 5 
b = -6

Therefore, the eqution of the parabola is y = 5x^2 - 6x + 1 .

6 0

3 years ago

What is the area of each triangle 24 ft 20 ft

arsen [322]

ANSWER

Area of triangle = b*h/2

24*20/2

24*10

The area of this triangle is 240 ft squared

Hope it helps :)

3 0

3 years ago

You use 240 cubic inches of clay to make a sculpture shaped as a rectangular prism. The width is 4 inches less than the length a

murzikaleks [220]

Answer:

L: 6

W: 2

H: 20

Step-by-step explanation:

First, we need to know the expression to calculate the volume of rectangular prism which is:

V = L * W * H

The only thing we know is that the volume is 240 in³ and that the width is 4in less than length, the height is 2 in more than 3 times length. So, everything is set in function of the length, therefore, we'll call L = x and then solve for x

L = x

W = x - 4

H = 3x + 2

Let's replace the data in the formula of volume:

240 = x * (x - 4) * (3x + 2)

240 = (x² - 4x)(3x + 2)

Solving this we have:

240 = 3x³ - 10x² - 8x

Rearranging the equation:

3x³ - 10x² - 8x - 240 = 0

Now, in order to solve this, we need to factorize the left side:

3x³ - 18x² + 8x² - 48x + 40x - 240 = 0

3x²(x - 6) + 8x(x - 6) + 40(x - 6) = 0

(x - 6)(3x² + 8x + 40) = 0

Now that we have this, we can solve the value of x.

x1 -----> x - 6 = 0 ---> x = 6

x2 ---> (3x² + 8x + 40) = 0

Δ = 8² - 4*3*40 = 64 - 480 = -416

This value of -416 means that it's not possible to get a real number as x (only the imaginary numbers), therefore the value of x should be 6

x = L = 6

With this value we can calculate W and H:

H = 6 - 2 = 4

W = (3*6) + 2 = 20

7 0

3 years ago